Is there a way to simplify the following equation?
$$\int_{-\infty}^{\infty} f(q) \delta(q-k) * g(q) dq =\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} f(q) \delta(q-k) g(q-\tau) d\tau dq $$
The $*$ is the convolution symbol and $\delta$ is the Dirac delta function.
Is it allowed to first do the integration and then the convolution to obtain:
$$\int_{-\infty}^{\infty} f(q) \delta(q-k) * g(q) dq \stackrel{?}{=} f(k)*g(k)$$